Using Exponential NotationWrite using exponents.
(a)
3 factors of 4Read as “4 43 cubed.”
4 # 4 # 4 = 43
EXAMPLE 1
24 CHAPTER 1 Review of the Real Number System
OBJECTIVES Two or more numbers whose product is a third number are factorsof that third number.
For example, 2 and 6 are factors of 12, since
OBJECTIVE 1 Use exponents.In algebra, we use exponentsas a way of writing
products of repeated factors. For example, the product is written as
follows.
5 factors of 2The number 5 shows that 2 is used as a factor 5 times. The number 5 is the exponent,
and 2 is the base.
ExponentBaseRead as “2 to the fifth power,” or “2 to the fifth.” Multiplying five 2s gives 32.
25 = 2 # 2 # 2 # 2 # 2 = 32
25
25
2 # 2 # 2 # 2 # 2 = 25
2 # 2 # 2 # 2 # 2
2 # 6 = 12.
Exponents, Roots, and Order of Operations
1.3
1 Use exponents.
2 Find square roots.
3 Use the order of
operations.
4 Evaluate algebraic
expressions for
given values of
variables.NOW TRY
EXERCISE 1
Write using exponents.
(a)
(b)t#t#t#t#t
1 - 321 - 321 - 32
Exponential ExpressionIf ais a real number and nis a natural number, then
nfactors of awhere nis the exponent,ais the base,and is an exponential expression.
Exponents are also called powers.
an
ana#a#a# Á #a,
(c)
Read as “ to the fourth power,” or “ to the fourth.”
(d) (e)
NOW TRYNOTE In Example 1,we used the terms squaredand cubedto refer to powers of 2
and 3, respectively. The term squaredcomes from the figure of a square, which has the
same measure for both length and width, as shown in FIGURE 17(a). Similarly, the term
cubedcomes from the figure of a cube, where the length, width, and height have the
same measure, as shown in FIGURE 17(b).
1 0.3 21 0.3 21 0.3 21 0.3 21 0.3 2 = 1 0.3 25 x#x#x#x#x#x=x^6
1 - 624 - 6 - 6
1 - 621 - 621 - 621 - 62 = 1 - 624
(b) 2 factors of
Read as A^35 B “^35 squared.”
23
53
5
#^3
5
= a
3
5
b
2NOW TRY ANSWERS
- (a) 1 - 323 (b)t^5
⎧⎪ ⎪⎨ ⎪⎪ ⎩
⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩